Space of modular forms of level 1134, weight 2, and Character 1134.l

• Label: 1134.2.l
• Level: $1134$
• Weight: $2$
• Character orbit: 1134.l
• Rep. character: $\chi_{1134}(215,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $64$
• Newform subspaces: $8$
• Sturm bound: $432$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.l (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(432\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1134, [\chi])\).

	Total	New	Old
Modular forms	480	64	416
Cusp forms	384	64	320
Eisenstein series	96	0	96

Trace form

\( 64 q - 64 q^{4} - 10 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1134, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1134.2.l.a	$1134$	$2$	1134.l	63.i	$6$	$4$	$2$	$9.055$	\(\Q(\zeta_{12})\)	None		$4$	$1$	\(0\)	\(0\)	\(0\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}^{3}q^{2}-q^{4}+(-2\zeta_{12}-2\zeta_{12}^{3})q^{5}+\cdots\)
1134.2.l.b	$1134$	$2$	1134.l	63.i	$6$	$4$	$2$	$9.055$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}^{3}q^{2}-q^{4}+(-\zeta_{12}-\zeta_{12}^{3})q^{5}+\cdots\)
1134.2.l.c	$1134$	$2$	1134.l	63.i	$6$	$4$	$2$	$9.055$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}^{3}q^{2}-q^{4}+(-\zeta_{12}-\zeta_{12}^{3})q^{5}+\cdots\)
1134.2.l.d	$1134$	$2$	1134.l	63.i	$6$	$4$	$2$	$9.055$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}^{3}q^{2}-q^{4}+(3-2\zeta_{12}^{2})q^{7}+\cdots\)
1134.2.l.e	$1134$	$2$	1134.l	63.i	$6$	$8$	$4$	$9.055$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{24}^{3}q^{2}-q^{4}+(\zeta_{24}^{5}-\zeta_{24}^{6})q^{5}+\cdots\)
1134.2.l.f	$1134$	$2$	1134.l	63.i	$6$	$8$	$4$	$9.055$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{24}^{3}q^{2}-q^{4}+(\zeta_{24}-2\zeta_{24}^{3}+\zeta_{24}^{5}+\cdots)q^{5}+\cdots\)
1134.2.l.g	$1134$	$2$	1134.l	63.i	$6$	$16$	$8$	$9.055$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{4}+\beta _{9})q^{2}-q^{4}+(\beta _{1}+\beta _{12}-\beta _{14}+\cdots)q^{5}+\cdots\)
1134.2.l.h	$1134$	$2$	1134.l	63.i	$6$	$16$	$8$	$9.055$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{4}-\beta _{9})q^{2}-q^{4}+(-\beta _{1}-\beta _{12}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1134, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1134, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 2}\)